(r-6)(r-2)=

Solution for (r-6)(r-2)= equation:

Simplifying
(r + -6)(r + -2) = 0

Reorder the terms:
(-6 + r)(r + -2) = 0

Reorder the terms:
(-6 + r)(-2 + r) = 0

Multiply (-6 + r) * (-2 + r)
(-6(-2 + r) + r(-2 + r)) = 0
((-2 * -6 + r * -6) + r(-2 + r)) = 0
((12 + -6r) + r(-2 + r)) = 0
(12 + -6r + (-2 * r + r * r)) = 0
(12 + -6r + (-2r + r2)) = 0

Combine like terms: -6r + -2r = -8r
(12 + -8r + r2) = 0

Solving
12 + -8r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + -1r)(6 + -1r) = 0

Subproblem 1
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {2, 6}